FIG. 1 illustrates a simple lens system 100 in which a lens 102 focuses an image of an object 104 onto an image plane 106. The object 104 is a front focus distance ff from the lens, while the image plane 106 is a back focus distance fb from the lens. For the lens 102 to maintain an optimally focused image on the image plane 106, the laws of optics dictate a certain relationship between ff and fb—in other words, for a given ff there is a specific value of fb that must be maintained for an image to be properly focused on the image plane 106.
What is true of the very simple lens system 100 is also true of more complex focusing systems: for a given ff there is a specific value of fb that must be maintained. In devices including more complex focusing elements, however, various factors such as thermal expansion, mechanical part tolerances, and the like may cause the focusing elements to move, thus altering the values of ff and fb and affecting the quality of the focused image. To correct these movements of the focusing elements, some devices incorporate movable optical elements whose positions are controlled by a control system. The control system senses when the image is going out of focus and adjusts the position of the movable optical elements until ff and fb are returned to their proper values and, as a result, the image is returned to optimal focus.
Before a control system can work properly, though, it must have some way of detecting the position of the movable optical element. The most common way of detecting the position of the movable optical element uses mechanical sensors. Mechanical sensors, however, tend to be bulky, expensive, and difficult to integrate into small systems. Since they are mechanical, their accuracy is also limited because of mechanical tolerances within the sensor and, moreover, the sensors are also subject to inaccuracies brought on by factors such as thermal expansion. Optically-based position sensors have been developed, but these are also bulky and expensive and depend mostly on measuring the front focal distance ff by, for example, transmitting and receiving a signal and measuring the delay to compute the distance. There is therefore a need in the art for an apparatus and method that accurately measures positions of a movable focusing element while being inexpensive, compact, and easy to integrate into optical systems.